On nonlinear systems—chaos
✍ Scribed by Y.H. Ku; Xiaoguang Sun
- Book ID
- 103091734
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 598 KB
- Volume
- 326
- Category
- Article
- ISSN
- 0016-0032
No coin nor oath required. For personal study only.
✦ Synopsis
Two nonlinear systems which exhibit chaotic characteristics are analysed with the aid of computer graphics. The first system is represented by the Lorenz equations involving three variables X, y and z. The second system is known as the double scroll given by an electric circuit involving the voltages V,, and V,,, and the current i,, with two capacitances C, and C2, an inductance L, one resistance G and a nonlinear resistor with piecewise Iinear characteristic. For the first system, projections of the 3-dimensional traj'ectory are given onto the z:x, z-y and y-x phase planes obtained with the aid of computer graphics. Similarly, the phase plane projections onto the x-x, jr-y and i-z planes are presented, with the projections onto the i-i, 9-i and i-9 phase $lanes. For the second system, one can get the projections onto the Vc,-i,, VcZ-iL and VcZ-Vc, phase planes. By suitable transformations the state equations jar the double scroll can be expressed in terms of the variables X, y and z. Projections onto the z-x, y-x and z-y phase planes are presented. Similarly, projections onto the i-x, jry and i-z phase planes are given, together with the projections onto the i-k, jl-jc and i-ji phase planes. The solution curves X, y and z for the Lorenz equations are shown. For the double scroll, x, y and z curves and their derivatives i, jl and i are also presented.
📜 SIMILAR VOLUMES
A detailed analysis is undertaken to explore the stability and bifurcation pattern of the nonlinear Bloch equation known to govern the dynamics of an ensemble of spins, controlling the basic process of nuclear magnetic resonance. After the initial analysis of the parameter space and stability region